Scintillators - American Chemical Society

Article pubs.acs.org/JPCC

Kinetic Model of Energy Relaxation in CsI:A (A = Tl and In) Scintillators S. Gridin,*,†,‡ A. Belsky,*,† C. Dujardin,† A. Gektin,‡ N. Shiran,‡ and A. Vasil’ev§ †

Institut Lumière Matière, Université Claude Bernard Lyon 1, UMR 5306 CNRS, 69622 Villeurbanne Cedex, France Institute for Scintillation Materials, 60 Lenin Avenue, 61001 Kharkov, Ukraine § Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1(2), 119991 Moscow, Russia ‡

ABSTRACT: A model of energy relaxation in alkali halide scintillators doped with Tl-like activators is presented. Interaction between thermalized charge carriers, their diffusion, and capture by traps are considered. The model of energy relaxation suggested in the work includes essential electron excited states in alkali halides doped with Tl-like activators. Self-trapping of holes occurs in alkali halides at LNT, giving rise to creation of self-trapped excitons (STEs). Thallium-like activator impurity can act both as an electron or a hole trap. Once both of the charge carriers are trapped by the dopant, activator recombination channel comes to action. The model is verified using CsI classical scintillation crystals doped with thallium and indium ions in a range of concentrations from 10−4 to 10−1 mol %. Temperature dependences of the STE and the activator-induced emission yield are measured as a function of the activator concentration under continuous X-ray excitation. A system of rate equations is used to simulate the applicability of the model under different excitation conditions. Evaluation of the parameters of the system is done for a numerical solution. The model of energy relaxation suggested allows to explain energy losses in CsI:A scintillators in a 10−300 K temperature range.

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INTRODUCTION A scintillation material aims to convert efficiently absorbed ionizing radiation into visible or ultraviolet photons that are detected using photodetectors such as photomultiplier tubes or cameras, depending on the application. They are therefore widely used in various fields such as medical imaging, monitoring the transportation of radioactive materials, or oil exploration. The yield of this conversion is a critical aspect because it drives the detection efficiency and its correlated properties such as the energy resolution and the timing of the overall detection system. In many cases, these materials are inorganic crystals containing an activator as dopant. A crude description is to consider the host as passive media where the primary interaction with the ionizing particle occurs, and the activator gives to this media its active property of light emission. The energy conversion from a single particle of hundreds of kiloelectronvolts to thousands of low-energy photons is of high complexity, and one of the challenges faced is to identify the losses that make the efficiency of scintillators lower than expected. Alkali halide scintillators (mainly CsI and NaI families) play a particular role. Because of their relatively high efficiency and low production cost, they are widely used and have been developed at the industrial level, providing reproducible materials. Attempts to model the scintillating processes were done using both analytical and numerical techniques.1−5 However, the proposed models were applied to explain only experiments done under specific conditions, e.g., at room temperature (RT). In addition, it appears that the spent © 2015 American Chemical Society

materials, despite their relative efficiency, are less efficient than expected. Indeed, the efficiency of the intrinsic emission of selftrapped excitons (STE) in undoped CsI and NaI is very high at low temperatures. According to light yield measurements, CsI pure samples emit up to 107 000 photons/MeV,6 and the emission yield for NaI pure crystals was found to be as high as 80 000 photons/MeV.7,8 Such efficiency, especially for pure CsI, is close to the fundamental limit for alkali halides.9 Unfortunately, these STE emissions are quenched at room temperature, rendering the interest in their application rather limited. In contrast, the light yield of the best activated CsI:Tl crystals is only about 60 000 photons/MeV.10,11 This indicates that about 44% of the potential yield is lost despite research and development of crystal growth performed worldwide and at a large scale. This suggests the existence of an intrinsic behavior that we aim to describe in this contribution. In addition, the scintillation yield of conventional activated alkali halide scintillators CsI:Tl, NaI:Tl, and CsI:Na decreases at temperatures below 80 K. According to our recent studies, the efficiency of CsI:Tl at 20 K is only about 20% of its maximum yield.12,13 In more detail, the scintillation process can be conveniently divided into three consecutive stages. The first stage, which includes primary interaction with an ionizing particle, electron− Received: June 12, 2015 Revised: August 11, 2015 Published: August 14, 2015 20578

DOI: 10.1021/acs.jpcc.5b05627 J. Phys. Chem. C 2015, 119, 20578−20590

Article

The Journal of Physical Chemistry C

X-ray-excited luminescence was detected by an ANDOR Newton CCD combined with a Shamrock 500i spectrograph. A 150/300 diffraction grating was used. The numerical solution of the system of kinetic differential equations was obtained using Wolfram Mathematica 8.5 software.

electron scattering, and Auger processes, results in the creation of hot electron−hole pairs. It concludes with the thermalization of hot electrons and holes through interaction with phonons. This first stage is more or less insensitive to activators, and we expect the situation to be the same in doped and undoped materials. When thermalized, these electronic excitations will diffuse and migrate in the crystal. In the end, they are captured by some traps or activators. Capture of both an electron and a hole at a trapping center can result in either radiative or nonradiative e−h recombination. Total scintillation efficiency can be described as a product of the efficiencies of each stage:14 η = βSQ

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MODEL DESCRIPTION For a correct and complete description of the scintillation processes in CsI:A, a general model of energy relaxation is proposed. It takes into account all the most important features of the luminescence centers and the system parameters. As described above, at the end of the thermalization stage, charge carrier migration occurs (S term in eq 1). During this stage, localization of the thermalized charge carrier takes place at capture centers, including luminescence centers. When this happens, radiative recombination may occur in competition with various potential nonradiative recombinations, including energy transfer leading to the quantum efficiency Q (eq 1). All these processes are closely connected and depend strongly on the parameters of the system, particularly on the luminescence centers and traps of charge carriers. In the following section, a detailed description of the final energy relaxation stage is provided, including all the activator charge states, as well as the intrinsic relaxation channel in CsI:A. General Scheme of the Electron Excited States. On the basis of the analysis of experimental works and considerations presented above, a general model of energy relaxation in activated alkali halides is proposed and shown in Figure 1.

(1)

where β is the efficiency of electron−hole creation (the conversion efficiency), S is the transfer efficiency, and Q is the luminescence quantum efficiency. The primary stages of the scintillation process determine the spatial distribution of electron−hole pairs in the excited region, leading to an initial spatial distribution of electrons and holes along the track and to the β factor. Modeling of the thermalization stage in alkali halides has been extensively developed recently.15 Firstprinciple calculations using the Monte Carlo method can give the energy distribution of secondary excitations.4,5 It was shown that peculiarities of the electron−hole recombination strongly depend on their respective spatial distribution at the end of the thermalization stage.16 However, accounts of interactions between thermalized charge carriers and luminescent centers are necessary to describe accurately the scintillation efficiency from the activator concentration in alkali halide scintillators.13 We assert that the final stages of the scintillation process, i.e., migration of charge carriers, their localization at the luminescence centers, and consequent radiative (or nonradiative) relaxation, are the key phenomena explaining the observed losses between pure and doped CsI. We propose a model of this final scintillation stage (migration and relaxation) able to describe, in the case of doped and undoped CsI, the role of the activator and to reproduce the evolution of the yields as a function of temperature. The proposed model takes into account the migration of charges and capture parameters of trapping centers, their temperature stability, and radiation time constant as well as the self-trapping of holes and excitons. To experimentally support our model, we compared pure CsI and CsI doped with two activator types: Tl and In. Both activator ions have s2 electron configurations. As a consequence, they exhibit similar luminescence properties.17 However, as it was found in ref 12, the fact that the parameters of the activator ions charge carriers capture are significantly different will provide a test of the validity of the model.

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Figure 1. Band model of electronic excitations in alkali halide scintillators doped with activator A. The model accounts for the time evolution of the concentration of (1) free electrons (electrons in the conduction band), (2) free holes (holes in the valence band), (3) selftrapped holes (STH), (4) self-trapped excitons, i.e., electrons trapped by STH (STH + e− = STE), (5) electrons trapped by activator ions (A+ + e− = A0), (6) holes trapped by activator ions (A+ + h+ = A2+), and (7) excited states of the activator centers (A+)*, which are created if either an electron is trapped by A2+ center (A2+ + e− = (A+)*) or a hole is trapped by A0 center (A0 + h+ = (A+)*).

EXPERIMENTAL AND ANALYTICAL METHODS

Concentration series of CsI:Tl and CsI:In single crystals were synthesized as described in ref 17. The activator concentration was measured using inductively coupled plasma atomic emission spectroscopy. For luminescence measurements, 1 mm thick discs were cut from the crystalline ingots and polished with an optical quality. To measure temperature dependences of X-ray-induced luminescence and thermostimulated luminescence (TSL) curves in the 10−300 K range, samples were mounted in a closed-cycle helium cryostat. An X-ray tube with tungsten anode run by an INEL XRG3000 X-ray generator was used for irradiation. The anode voltage was set to 35 kV.

Under exposure to ionizing radiation, free electrons and holes are created. These free charge carriers can recombine as follows: Free holes h+ can be self-trapped or captured by neutral activator centers A+, corresponding to the natural valence state of the two ions considered in this work, e.g., Tl+ or In+. The A center may also be stable as A0, which can thus trap a hole as well, leading to A+*. Both processes can be summarized as A+ + h+ → A2+ and A0 + h+ → (A+)*. Similarly, free electrons e− can be captured by activator centers A+ + e− → A0 or A2+ + e− → (A+)*. A free electron can also be trapped by STH to form a self-trapped exciton (STH + e− → STE). 20579


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Figure 2. Contribution to the rate of free holes h+, free electrons e−, and excitons in CsI:A created as a result of interaction with ionizing radiation γ.

coefficient. The reverse process corresponding to thermal activation of C contributes through the well-know term +sC nC(t) exp(−AC/(kT)). The term sC is the frequency factor, whereas AC is the thermal activation energy. Note that the reverse process is not considered for (A+)* and STE because they naturally rapidly decay radiatively or nonradiatively. Apart from the radiative decay rate, all contributions to the population rates are indicated in Figure 2, and the full system of rate equations for CsI:A (hereinafter referred to as the System) is presented in Appendix A. Consequently, the complete System of rate equations (Appendix A) consists of seven equations for the seven rates of contributing species in CsI:A crystal. Such a System does not have an analytical solution. However, a numerical solution can be found if initial conditions and parameter values are set. Many of the parameters can be eliminated from the experiment, and others can at least be estimated.

Reverse processes can occur through thermal activation and are shown as green arrows in Figure 2. In the temperature range we consider (10−300 K), both (A+)* and STE can lead to radiative recombination with time characteristics τA and τSTE according to (A+)*→ A+ + hν 550 nm and STE → hν 340 nm. Note that STE exhibit a thermal quenching in this temperature range, so we also introduce τnr(T) in the set of equations driving the populations. Both of these processes are indicated in Figure 1. Finally, the model accounts for a fraction of excitations that instantly form excitons (so-called direct creation of excitons).16 Mathematical Modeling of Energy Relaxation. For mathematical modeling of energy relaxation presented in the previous section and in Figure 1, a system of rate equations has been composed. This approach to describing the luminescence kinetics of crystal phosphors was initially developed in the 1960s by Antonov-Romanovskiy and Fok.18,19 For some simplified cases, analytical solutions were obtained. Recently, this method of kinetic modeling of energy relaxation processes was used to describe energy relaxation processes in other scintillation crystals.20,21 In the latter works, mathematical modeling is done using some numerical methods to solve the equations. The system of rate equations describes changes in time for concentrations of free electrons ne, free holes nh, self-trapped holes nSTH, electrons captured by activator centers nA0, holes captured by activator centers nA2+, self-trapped excitons nSTE, and excited activator centers nA+*. The scheme of interplay between the various elements is shown in Figure 2. The initial interaction with ionizing radiation γ leads to free holes, free electrons, and excitons. The creation rate of electrons and holes is written as αt(1 − rex) . Although αt is proportional to the flux of absorbed X-rays, the coefficient rex accounts for the probability of direct exciton creation. Here we consider that all electron−hole pairs separated by a distance smaller than a capture radius (Onsager radius) recombine in an exciton. In general, the interplay between the various species is because of bimolecular recombination and thermal activation. In the first case, the rate of A + B → C contributes to the population rate of A and B as −nA(t) nB(t) βA+B, where the ni(t) is the population of species i and βA+B is the bimolecular capture

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VERIFICATION OF THE MODEL The choice of CsI:A scintillators for model verification allows us to use the significant amount of experimental knowledge accumulated over the last few decades. In particular, regarding scintillation efficiency, three experimental facts require explanation. The first is the high efficiency of STE emission in CsI pure at LHeT. The second is the energy loss of 50% in activated CsI-based scintillation crystals at RT. The third is the intensity decrease of 80% observed in CsI:A at LHeT for the activator emission. The first effect suggests high efficiency of e− h pair creation (β) in CsI. Consequently, one can assume that the energy losses observed in CsI:A take place during the migration stage of the scintillation process (S). This suggests an important role of the intermediate charge states that are stabilized at low temperature. System Parameters Determination and Numerical Solution. Solving the set of equations depends on many parameters. The number of degrees of freedom is too large to apply a fitting procedure leading to meaningful physical parameters. We thus aim in this section to estimate all these parameters or to evaluate them from the experiment. Frequency Factors and Trap Depths. Energies of thermal release of charge carriers from traps (trap depths) as well as the 20580


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first-order kinetics Randall and Wilkins formula22 was used to fit the TSL peaks at 60, 90, and 115 K in CsI:Tl. The mean time a charge carrier spends in the trap at a given temperature can be deduced through

frequency factors of such delocalization can be derived from glow curve analysis.22 For CsI:Tl and CsI:In single crystals, we obtained these parameters of some traps using the initial rise method. Following X-ray irradiation over the course of 10 min, partial cleaning of the glow curve was done by heating the sample up to the temperature of peak maximum in order to separate the overlapping peaks and to see its initial rise profile.12 Table 1 presents the resulting parameters for Tl, In, and intrinsic traps in CsI. The abnormally high frequency factor and

τ=

peak temp. (K)

EA (eV)

CsI:Tl,CsI:In CsI:Tl,CsI:In CsI:Tl CsI:In

60 90 115 240

0.23 0.15 0.28 0.59

s (s−1)

kin. order

lifetime at 300 K (s)

× × × ×

1 1 1 1.6

10−4 1.4 × 10−6

4.8 3.0 3.3 1.1

1016 106 1010 1011

thermal energy of delocalization obtained for the peak at 60 K suggest a tunneling diffusion of holes to the luminescence centers. An alternative way to get more a meaningful estimation for activation energy of STH hopping motion (corresponding to 60 K glow peak in CsI:A glow curves) can be as follows. From general considerations, frequency factor s is usually on the order of the frequency of the longitudinal optical phonons (LO). In CsI, it is about 80 cm−1 ≈ 0.01 eV. Using the equation (βEA)/(kBT2m) = s exp(−EA/(kBTm)) known from TSL analysis and assuming s = 2.4× 1012 (from ELO(CsI) = 0.01 eV), activation energy of STH hopping motion EA(60 K) was evaluated to be 0.14 eV. It makes sense that this value is lower than EA(90 K) because activation of STH hopping diffusion should require less energy than their thermal release. As was pointed out earlier, the TSL peak at 60 K cannot be properly fitted by a standard glow curve.23 Contribution of the hopping motion of STHs (glow peak at 60 K) has been neglected as compared to the motion of free carriers (90 K peak) when solving the System of rate equations. These trap parameters, listed in Table 1, have been used to reconstruct the theoretical TSL for comparison with the experimental ones considered using heating rate T′ eq 2. Only the parameters of the glow peak at 240 K come from the fitting of the TSL experimental curve. Note that this glow peak around 240 K in CsI:In cannot be treated in terms of the first-order kinetics (when probability of recombination after detrapping is much higher than the probability of repetitive trapping of the carriers). Parameters of this peak were found by means of fitting the glow curve with the equation for general-order kinetics TSL intensity eq 2.22 The best match was obtained with the parameters given in Table 1, and the comparison between reconstructed glow curves is in agreement with the experimental one, except for the 60 K glow peak.

Figure 3. Fitting of (a) CsI:Tl and (b) CsI:In glow curves with eq 2 using trap parameters from Table 1.

Frequency factors and trap depths for holes captured by activator in CsI:A cannot be obtained from the glow curves because there are no TSL peaks corresponding to hole release from A2+. Indeed, the luminescence of a released hole requires a recombination with a A0 center that is not stable for temperatures higher than 115 K for CsI:Tl and 240 K for CsI:In.12,24 This suggests that the A2+ glow peak cannot be seen if it is predicted to appear at a higher temperature. As reported in ref 25, EPR methods revealed that holes were found to remain localized in Tl sites for a few minutes after heating the crystal up to RT. This result suggests that a Tl-related hole trap in CsI is rather stable at 300 K which confirms that its corresponding glow peak cannot be observed. We thus selected an order of magnitude for these parameters reproducing this property: Ah = 0.7 eV and sh = 1011 s−1 for CsI:Tl, and Ah = 1.0 eV, sh = 1011 s−1 for CsI:In. We checked that variations of these

⎛ − E ⎞⎡ ⎛ (b − 1)s″ ⎞ ⎟ I(T ) = n(0)s″exp⎜ A ⎟⎢1 + ⎜ ⎝ ⎠ T′ ⎝ kBT ⎠⎢⎣

∫T

T

0

b(b − 1) ⎛ −EA ⎞ ⎤ exp⎜ ⎟ dT ⎥ ⎝ kBT ⎠ ⎥⎦

(3)

We emphasize that depending on the temperature the lifetime in traps can be significant. Using the trap parameters from Table 1, we estimate the mean lifetime of STHs at 300 K to be about 10−4 s. For comparison, the lifetime of Tl0 centers is 1.4 × 10−6 s, which is 2 orders of magnitude shorter. It suggests that even at RT self-trapping of holes still occurs and that these STH can capture electrons with subsequent radiative/nonradiative STE recombination contributing thus to the loss of yield.

Table 1. Trapping Parameters in CsI:Tl and CsI:In crystal

⎛ E ⎞ 1 exp⎜ A ⎟ s ⎝ kBT ⎠

(2)

where b is kinetic order and n(0) is the concentration of filled traps. Equation 2 makes no sense for b = 1, so the standard 20581


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The Journal of Physical Chemistry C parameters do not further lead to a significant change in simulations of light yield temperature dependence and TSL of CsI:A in the region 10−300 K. Bimolecular Capture Coefficients. Parameter βij determines capture probability of charge carriers i by the center j. In the diffusion approximation, these coefficients can be expressed through diffusion coefficients and capture radii: βij = 4πDiRij, Here Di is the diffusion coefficient of the corresponding charge carrier, and Rij is the capture radius of carrier i by center j. Diffusion coefficients for electrons and holes depend significantly on temperature. Two types of diffusion apply for holes in CsI depending on temperature. The first is the hopping motion of self-trapped holes, which is true for holes in CsI below the delocalization point, and the second corresponds to the diffusion of free holes in the valence band. The hopping diffusion coefficient for holes can be written as Dhop = (1/ h 3)(a2hvh exp(−Ehop A /(kBT))), where ah is the distance of a single hop and νh is the frequency of hops. The value of ah can be estimated as a/√2, where a is the CsI lattice constant (0.47 nm). The frequency νh is often of the same order of magnitude as the frequency of the LO phonons in CsI, which corresponds to about 0.01 eV in energy. Activation energy of the hopping motion in CsI Ehop is about 0.13 eV, which provides the A diffusion coefficient of the hole’s hopping motion Dhhop negligible below 60 K. For free (delocalized) carriers, accounting of the scattering on phonons is necessary. For a carrier with energy E, the diffusion coefficient can be written as D(E, T) = (1/3)(v2/ (wtr(E, T))) = (2/3)(E/(m wtr(E, T))), where wtr(E,T) = wtr,LA(E,T) + wtr,LO(E,T) is the energy- and temperaturedependent transport scattering rate. After averaging with the Boltzmann distribution, the average diffusion coefficient Dfree(T ) =

1 kBT

∫0

∞

D(E , T )e−E / kBT dE

Figure 4. Diffusion coefficients of free electrons, free holes (m*e = m0 and mh* = 2.27 m0) in CsI as a function of temperature according to eq 4.

can be thus deduced as βe+A+ = 3.1 × 10−8 cm3 s−1 and βh+A+ = 1.2 × 10−8 cm3 s−1. In the case of electron or hole capture by charged centers, i.e., by self-trapped holes or by activator centers that have already trapped a carrier of the opposite sign, the capture radius is known as the Onsager radius,15,16 and for CsI at 80 K, ROns = 4 × 10−6 cm. This estimate of capture by charged centers leads to βSTE = βe+A2+ = 5.0 × 10−7 cm3 s−1 and βh+A0 = 2.0 × 10−7 cm3 s−1. Strictly speaking, the capture radius depends on temperature as 1/T. However, an increase of the capture radius at low temperature (10−60 K) will be compensated for by a decrease of the diffusion coefficient (Figure 4). Hence, in the present investigation, the constant values of bimolecular capture coefficients β are used. Other Parameters. STE radiation time in CsI τSTE (about 1 μs), as well as thermal quenching activation energy ESTE and frequency factor sSTE of STE nonradiative relaxation time 1/τnr = sSTE exp(−ESTE/(kBT)) were obtained by Lamatsch.29 ESTE was chosen to be 0.11 eV, and the frequency factor was taken to be 8 × 109 s−1. This allows an estimate of τnr of around 10 ns at 300 K. Radiative time of excited In and Tl activator centers τA was chosen as equal to 10−6 s, which is close to experimentally obtained values for CsI:Tl and CsI:In under intracenter photo excitation.17 The parameter αt, i.e., electon−hole pair creation rate, was estimated as follows. The X-ray photon flux received by the sample surface was 6.5 × 109 photons cm−2 s−1 . Considering the X-ray spectrum generated by a tungsten cathode and a voltage set at 35 kV, the attenuation length is estimated at around 10 μm.30 Energy efficiency of electron−hole pair creation in CsI is estimated as 1.6Eg, which is about 10 eV per e−h pair.13 One X-ray photon with an average energy of 21 keV thus creates 2100 e−h pairs in the crystal. Finally, average electron excitation creation rate in a 10 μm thick surface layer of CsI is estimated at about 1016 cm−3 s−1. Strictly speaking, e− h distribution is strongly nonhomogeneous in a real X-ray track. It contains low- and high-excitation-density regions with very different recombination conditions. In the present work, we are using this estimation of the average e−h creation rate as a simplification. A more refined model taking into account this nonuniformity is currently being developed. Parameter rex (direct creation of excitons) is typically on the order of 0.1 in inorganic scintillators; however in CsI, it can be significantly higher because of the higher fraction of low energy

(4)

Here we use standard formulas for the transport scattering rates wtr,LA and wtr,LO of electron−phonon interaction with longitudinal acoustical (LA) and LO phonons. They are discussed in more detail by Kirkin et al.15 The parameters for quantitative evaluation (also used by Wang et al.5) are listed in Table 2. Table 2. Some Constants of CsI26,27 parameter

value

static dielectric permittivity ϵ0 high-frequency dielectric permittivity ϵ∞ sound velocity Cs deformation potential σ optical phonon frequency ℏΩLO

5.65 3.00 1474 m s−1 0.53 eV 10 meV

Diffusion coefficients for free electrons and holes as a function of temperature estimated by eq 4 are presented in Figure 4. It is worth noting that the diffusion coefficient for free electrons in CsI obtained here for 300 K is 30 times lower than the estimate made in ref 28. As can be seen, the diffusion coefficient for free electrons and holes has the same order of magnitude between 40 and 300 K. It falls by an order of magnitude as the temperature goes down to 20 K. For the sake of simplicity, for the simulation we took De = 0.01 cm2 s−1 and Dh = 0.004 cm2 s−1 for the whole temperature range. The capture radius Re+A+ has already been estimated to be 2.5 × 10−7 cm.13 The capture coefficients by regular activator ions 20582


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Figure 5. Experimental temperature dependences of (a) STE 340 nm and (c) activator 550 nm emission channels in CsI:Tl under X-ray excitation for different activator concentrations in comparison with simulated curves for (b) STE and (d) activator yields. Curves are normalized to the maximum yield.

Figure 6. Experimental temperature dependences of (a) STE 340 nm and (c) activator 550 nm emission channels in CsI:In under X-ray excitation for different activator concentrations in comparison with simulated curves for (b) STE and (d) activator yields. Curves are normalized to the maximum yield.

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Figure 7. Concentration dependences of the STE and activator emission yield of (a) CsI:Tl crystals and (b) CsI:In at RT and LHeT.

electrons.16 In the present simulation, it was chosen to be 0.2. We emphasize that it is difficult to estimate rex here with high accuracy, and the impact of its variation will be discussed later. Comparison of Simulation and Experiment. Temperature Dependences. A comparison of experimental and simulated temperature dependences of STE (340 nm) and activator (550 nm) emission channels of CsI:Tl and CsI:In is presented in Figures 5 and 6, respectively. Activator concentrations for the simulated curves (panels b and d in Figures 5 and 6) were chosen close to the real activator concentrations in investigated crystals. A fair agreement between the experimental results and simulated curves is evident for both CsI:Tl and CsI:In. Simulated STE emission intensity tends to decrease as the temperature rises. Overall STE emission yield also drops as activator concentration increases (Figures 5a,b and 6a,b). The activator emission channel decreases at low temperature range. Activator energy losses in the 10−60 K temperature region (Figures 5d and 6d) are similar to those obtained in the experiment (Figures 5c and 6c). The simulated curves are modulated with similar valleys as the experimental dependences are. Those valleys correspond to the intense intrinsic and activator-related glow peaks in corresponding TSL curves, and are related to trapping of charge carriers. As the temperature reaches 90 K (glow peak of hole self-trapping in CsI), an evident decrease of the activator channel yield is observed in the simulated curves as well. We must note there are also some discrepancies between the experiment and the simulation that are noticeable in Figure 6. For example, in Figure 6a, the green curve goes higher than the red one, but in the simulation (Figure 6b), the red one is higher

than the green one. Most probably this difference is caused by some experimental error we had during measurement. Also, in Figure 6d, the yield is saturated at 0.8 at the high temperature regardless of the activator concentration, and the curve shapes of Figure 6d do not match well with those in Figure 6c. This discrepancy of simulation with the experiment can suggest that hole-trapping/release parameters for CsI:In might be not accurate enough. Overall, the temperature behavior and tendencies of scintillation yield obtained in the experiment are reflected in the simulation. This means that the model of energy relaxation presented in Figure 1 takes into account the most important processes of energy localization and relaxation in CsI:A. It also confirms that the parameters used for the numerical solution of the system of rate equations (Figure 2 and eq A7) were accurately estimated. Concentration Dependences. Now let us consider the processes that determine scintillation efficiency of the investigated scintillation system at RT and at LHeT. Experimental concentration dependences of the X-ray luminescence yield in comparison to simulation results are given in Figure 7. At LHeT (20 K), STE emission intensity drops down quickly with activator concentration increase in CsI:Tl and CsI:In (Figure 7a,b) according to the experiment. In the case of CsI:Tl in particular, at an activator concentration of around 0.1% mol STE emission almost completely disappears. When it comes to simulated curves, however, STE channel yield at this activator concentration is still about 0.25. Simulated concentration dependences of the activator luminescence yield at RT are in good qualitative agreement 20584


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Figure 8. Temperature dependence of STE (a) and activator (b) luminescence yield in CsI:Tl as a function of direct exciton creation parameter rex (Simulation).

Figure 9. Temperature dependence of (a) STE and (b) activator luminescence yield in CsI:Tl as a function of excitation creation rate (simulation).

result in the creation of low-energy electron−hole pairs that would increase the fraction of excitons created. Excitations’ Creation Rate. The excitation creation rate α(t) strongly depends on the irradiation conditions. In our experiment it was estimated to be about 1015−1016 pairs cm−3 s−1. It was found that the temperature dynamics of emission channels in CsI:A strongly depend on this parameter (Figure 9). The simulation is done for CsI:Tl scintillator with 0.02% mol Tl. We checked the excitation creation rate value from 1013 to 1017 e−h pairs cm−3 s−1. At low excitation creation rates (about 1013), STE recombination yield is limited by rex (0.2% in the simulation), in accordance with Figure 9a. The activator yield below 100 K is very weak (Figure 9b). Because distribution of electron excitations is assumed to be homogeneous, electron and hole will be generated as diluted, with an initial e−h distance separation often larger than the capture radius. Consequently, the hole will be self-trapped, whereas the electron will be captured by an activator ion. Energy losses due to trapping of charge carriers are thus favorable in this case. Increase of the e−h creation rate reasonably leads to an increase of the STE recombination yield at temperatures below LNT (Figure 9a). However, an activator yield around (150− 300) K tends to decrease as soon as excitation density reaches the activator concentration in the crystal (Figure 9b). Account of Energy Transfer from STE to Activator. The overestimation of the STE channel of relaxation at temperatures close to RT might be due to either the presence of some additional channel of nonradiative STE relaxation related to the activator or energy transfer from STE to the activator as suggested in ref 13. Nonradiative energy transfer, also referred to as Forster resonance energy transfer (FRET), is a common phenomenon in many scintillators. Its efficiency is proportional

with the experiment (Figure 7). At high activator concentrations (0.02−0.1% mol), the simulated activator luminescence yield is mostly stable and saturated, as the experimental curves show. At very low activator concentrations (below 0.01% mol for CsI:Tl and below 0.005% mol for CsI:In), simulated activator yield falls off, which quite closely follows the experimental data. Variation of Parameters. Even though the model was found to adequately describe scintillation efficiency of CsI:A as a function of temperature and activator concentrations, there are still some quantitative differences as highlighted in Figures 5 and 6. The simulation somewhat overestimates the STE recombination channel at relatively high activator concentrations. In addition, an activator emission yield at around 300 K makes about 80% of STE efficiency that is also overestimated. According to the experimental results, the activator emission yield at 300 K in CsI:A is about 50% of STE. Keeping in mind that some of the system parameters are roughly estimated, the following section discusses the sensitivity of the efficiency of the intrinsic and activator relaxation channels in CsI:A to the values of the parameters. Direct Creation of Excitons. The fraction of direct creation of excitons rex was estimated as 0.2 for CsI. (See last paragraph of section titled “Other Parameters”.) More accurate evaluation of this parameter is difficult. The increase of rex naturally modifies the balance between activator and STE channel in favor of the latter (Figure 8a,b). The fraction of activator energy losses within the 150−300 K temperature region basically corresponds to rex. Setting it to 0.4−0.5 allows us to reproduce activator emission yield around RT. It was noted earlier that the value of this parameter in CsI can be higher in view of the band structure of CsI.16 Auger decay of 5p Cs core holes should 20585


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ature range 150−300 K. Fast intrinsic luminescence (FIL) peaking at 300 nm has been observed in CsI.32,33 The nature of this emission is not completely clear; this is why we cannot take it into account in the initial System of equations. Nevertheless, it contributes to the detected signal. The temperature quenching of the FIL may contribute to the observed difference between simulation and activator yield. The X-ray-excited luminescence yield temperature dependence of this band is shown in Figure 11. At low temperatures (15−80 K), the

to the overlap between the donor’s emission spectrum and the acceptor’s excitation spectrum.31 In the case of CsI:A, it can occur as STE → Activator. The impact of such energy transfer on the simulation is shown in Figure 10. Here dipole−dipole

Figure 10. Change in STE and activator yield concentration dependence produced by account of energy transfer between STE and Tl emission (simulation).

Figure 11. Temperature dependences of the scintillation yield of STE (340 nm) and FIL (300 nm) emission in pure CsI. STE (340 nm) emission intensity under direct excitation form.34

energy transfer between STE and Tl+ centers is assumed. The transfer fraction is expressed in the following way. Decay kinetics of the excitonic channel in the case of dipole−dipole energy transfer can be described by the well-known formula ⎛ t t ⎞ ⎟⎟ nex (t ) = nex (0) exp⎜⎜ − − 2q τR ⎠ ⎝ τR

overall yield of the intrinsic emission is mainly due to the STE (340 nm) luminescence, whereas the intensity of the FIL band (300 nm) is negligible. As can be seen from Figure 11, STE luminescence temperature dependence under X-ray excitation is in good agreement with the curve in ref 34 obtained under direct excitation of excitons. FIL emission intensity reaches its maximum yield at about 150 K. At this temperature, the yield is about 20% of the maximum efficiency. Further temperature increase results in continuous decrease of the FIL luminescence yield. At 300 K, it amounts to about 2−5% of the maximum. Nevertheless, the slope of the luminescence yield temperature dependence around 150−300 K can be explained by the FIL temperature quenching that is also observed through the decay under monochromatic X-ray excitation as a function of temperature (Figure 12). According to Figure 12, at 145 K (when luminescence yield FIL is maximal) there is at most one exponential component in the scintillation decay. As the temperature goes up, the decay kinetics of this luminescence is greatly accelerated. In addition, the acceleration of the decay kinetics is accompanied by a

(5)

where we introduce the dimensionless FRET parameter q = (2π(3/2)Rd−d3nA)/3, Rd−d is the radius of dipole−dipole transfer, nex(0) is the initial concentration of excitons, and τR is the exciton’s radiation lifetime. Integrating eq 5 over t, we can estimate the concentration of excitons that decay radiatively. In this way, we can also calculate the fraction of activators to which excitons transfer the energy FA =

π q exp(q2) (1 − Erf (q))

(6)

where Erf(x) is the error function. In the case of energy transfer from quenched excitons (for any temperatures), the temperature dependent FRET parameter q = (2π(3/2)Rd−d3nA)/(3[1 + (τR/(τQ(T)))](1/2)), where τR and τQ(T) are the exciton radiation and nonradiation lifetimes, respectively. The fraction of radiatively decayed excitons is FR = (1 − FA)/[1 + (τR/ (τQ(T))]. As can be observed in Figure 10, an account of the energy transfer (using eq 6 with Rd−d = 3 nm) results in a decrease of the STE intensity correlated with the increase of the activator yield. The decrease of the excitonic channel intensity (experimental and simulated curves at 20 K in Figure 7) is as expected, accompanied by some increase of the activator emission yield. However, the total radiative recombination yield (excitonic and activator-related) is much lower than unity at high activator concentrations. This effect is also reflected in the simulation, and it originates from the trapping of electrons by activator ions whereas holes become self-trapped in the CsI lattice. Temperature Quenching of FIL in CsI. As can be seen from a comparison of the experimental and simulated curves (Figures 5 and 6), the activator luminescence yield of CsI:A is somewhat overestimated in the simulations in the temper-

Figure 12. Scintillation decay curves for FIL 300 nm emission measured under 1000 eV monochromatic X-ray excitation as a function of temperature. 20586


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The Journal of Physical Chemistry C deviation from the exponential law. The acceleration observed for the FIL luminescence decay indicates nonradiative relaxation of the FIL excited state with temperature increase. We emphasize that the 300 nm FIL emission band overlaps the A absorption band in CsI:Tl and CsI:In. Thus, radiative or nonradiative energy transfer from FIL excited state to the activator centers is allowed. The probability of the resonant transfer will be strongly dependent on the activator concentration (eq 6). In addition, a competition between activator centers and the FIL excited state in terms of charge carrier capture can also occur. Nevertheless, the FIL nonradiative relaxation channel may cause up to 20% of energy loss at RT in CsI:A scintillators. An account of this effect in case all the energy from FIL state is transferred to the activator is shown in Figure 13. One can see that the account of the energy transfer FIL → Activator enables us to better reproduce the shape of the activator emission yield between 150 and 300 K.

Figure 14. Simulation of STE emission (red), activator emission (blue), and fraction of quenched STEs (black) as a function of temperature.

some migration energy loss to the separated electron−hole excitations. The energy loss in CsI:A at low temperatures can be explained by trapping of e− and h+ by different lattice defects. For temperatures below the hole self-trapping glow peak (90 K in case of CsI), cross-trapping of charge carriers occurs, i.e., electrons are trapped by activator ions, but holes become instantly self-trapped. Simulation of this effect of energy storage in CsI:Tl is presented in Figure 15. As the temperature goes

Figure 13. Simulated activator emission yield at rex = 0.4, FIL output in pure CsI, and their sum as a function of temperature, compared with the experiment.

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ENERGY LOSS CHANNELS IN CSI:A Let us now try to explain the major features of CsI:A scintillation yield as a function of activator concentration and temperature on the basis of the proposed model. We shall focus on two key aspects according to the experimental curves in Figure 7. First, activator yield of X-ray-induced luminescence in CsI:A at 300 K is about two times lower than the maximum STE emission yield in pure CsI. Second, total emission intensity in highly doped CsI:A crystals at LHeT is about 0.2− 0.3, compared with STE maximum yield. These energy losses can be explained in the framework of the proposed model of energy relaxation in CsI:A, without using additional channel(s) of nonradiative relaxation. The energy loss in CsI:A at 300 K can be explained partially by STE quenching. Simulated radiative and nonradiative relaxation processes in CsI:Tl (0.1% mol Tl) are shown in Figure 14. STE quenching becomes significant above 100 K, and about 20% of all the electron excitations undergo nonradiative recombination in the form of thermal quenching of STE. The predominant fraction of created STE here are those created by direct recombination. The fraction of these directly created excitons created in CsI under X-ray may be quite significant. As discussed in ref 16, a high fraction of lowenergy electrons is generated in the 5p Cs band through the Auger process in CsI. However, it is possible that some additional channel of nonradiative relaxation (some sort of lattice defects perhaps) is in fact present in CsI:A, and it causes

Figure 15. Energy storage in CsI:A at low temperatures. Holes become self-trapped, and electrons are trapped by activator centers.

down and reaches the point of thermal release of electrons from Tl sites, the number of electrons captured by the activator (Tl0 centers) starts to increase. This goes along with an equivalent increase of the number of activator captured holes (Tl2+ centers). Once the temperature is low enough for efficient STH creation (around 90 K in CsI), the number of STHs starts to increase (black curve in Figure 15). Along with this, growth of Tl2+ center concentration becomes slower, and at some point, their content starts decreasing because self-trapping of holes becomes more efficient. Glow peak positions of the TSL simulation curve correspond to the peculiarities of X-ray luminescence temperature dependences (gray dashed line in Figure 15). Extrapolation of the curve for capture electrons on the temperature axis (black dotted curve in Figure 15) gives an electron-trapping rate of 1.2 × 1015 electrons cm−3 s−1 under particular irradiation and cooling conditions. Given the e−h pair creation rate α(t) = 2 × 1015 e−h cm−3 s−1, the radiative relaxation channel loses more than half of electron excitations created. Indeed, as it follows from experimental and simulated 20587


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Figure 16. Graphical solution of the problem of energy losses and relaxation in CsI:A: (a) pure crystal, (b) activated crystal below 80 K, and (c) activated crystal at RT. The thickness of the branches corresponds to the recombination efficiency of each channel.

CsI:A at T < 80 K (Figure 16 b). (c) At T > 150 K, selftrapping of holes in CsI is not efficient. In activated crystals (c > 0), separated e−h pairs are mostly captured by the activator centers. However, excitons are also created, mainly by means of direct e−h recombination. Losses in scintillation efficiency of CsI:A can be in part explained by nonradiative STE relaxation (Figure 16 c).

temperature dependences of activator yield in CsI:Tl (Figure 7 a), below 60 K at 0.1% mol Tl STE and activator channels together give less that 50% of maximum emission efficiency. Overall, our model of energy relaxation processes in CsI:A permits a satisfactory numerical simulation of intrinsic and activator scintillation efficiency as a function of temperature and activator concentration. The account of charge carrier capture parameters by luminescence centers for CsI:Tl and CsI:In crystals allowed us to simulate adequately many properties as a function of temperature and activator concentration. These include the X-ray-induced luminescence intensity temperature dependences and concentration dependences of the yield. The efficiency of radiative relaxation channels and energy loss channels in CsI:A strongly depends on the system parameters. Depending on temperature and the activator content, the following energy relaxation mechanisms can be marked out in CsI:A: (a) In pure CsI crystals (c = 0), the mechanism of energy relaxation is the creation of STEs. The only channel of energy loss is temperature quenching of STEs. At low temperatures (T < 80 K), maximum scintillation efficiency is reached because there are no other channels of energy losses (Figure 16 a). (b) In activated CsI:A crystals (c > 0), there are two channels of relaxation: excitonic and activatorinduced. At T < 80 K, a decrease of the scintillation yield occurs because of storage of noncorrelated charge carriers on stable traps: self-trapping of holes and electron capture by activator centers A+ with creation of A0. Release of charge carriers from these traps gives intense glow peaks in TSL curves. Energy storage is the reason for scintillation efficiency decrease in

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CONCLUSIONS In this work, we propose a model of energy relaxation in CsI:A that is based on experimental study of the scintillation crystals. The model takes into account main electron excited states in CsI:A giving rise to intrinsic (STE) and activator relaxation. Three charge states of the activator (A+, A0, and A2+) are taken into account. The only channel of nonradiative relaxation is STE temperature quenching. A System of rate equations was established to describe the dynamics of energy relaxation processes in CsI:A. The modeling approach applied is rather general and can be used for a large variety of scintillation materials. Appropriate modification of the rate equations will be needed as well as some experimental data for estimation of parameters. It is shown that detailed and accurate evaluation/estimation of the parameter of the system permits reasonable simulations of many scintillation properties of CsI:A. Energy losses in CsI:A that limit scintillation yield at RT can be related to nonradiative relaxation of STE. A significant fraction of spatially correlated electron−hole pairs form excitons and nonradiatively recombine at RT. STE creation 20588


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⎛ −A A++ ⎞ dn A++(t ) ⎟ = βh + A+nh(t ) n A+(t ) − s A++n A++(t ) exp⎜ ⎝ kT ⎠ dt

and quenching at RT is an intrinsic property of classical alkali halide scintillators CsI and NaI. This means that energy losses cannot be avoided in CsI:A at RT. We highlight that this conclusion thus has a significant impact regarding optimization of these materials for scintillating detector optimization. Efficient nonradiative energy transfer between STE and Activator emission centers could be one of the reasons for extremely high efficiency of Eu-doped alkali earth halide scintillators. Investigation of the nonradiative energy transfer efficiency from intrinsic to activator luminescence centers in alkali earth halides in comparison with the classical alkali halides could be an interesting area for further study. Numerical modeling of energy relaxation processes in CsI:A applied in this work has some limitations and simplifications. We assume that the density of electronic excitations is homogeneous in the crystal, which is not the case under Xray or γ excitation. The ionization particle track contains highexcitation-density regions with a distance between excitation of under 3 nm, where energy losses occur because of concentration quenching. The fraction of such high-excitation-density regions depends on the energy of the incident irradiation. Further development of this modeling method is possible by taking into account the spatial distribution of electronic excitation in the excited region of scintillators. This will broaden the applicability of the mathematical method of analysis used in this work.

− βe + A++ne(t ) n A++(t )

dnSTE(t ) n (t ) n (t ) = βSTEne(t ) nSTH(t ) − STE − STE τnr τSTE dt + αt rex

dne(t ) = αt (1 − rex ) − βe + A+ne(t ) n A+(t ) dt − βe + A++ne(t ) n A++(t ) − βSTEne(t ) nSTH(t ) (A1)

dnh(t ) = αt (1 − rex ) − βSTHnh(t ) nST(t ) dt − βh + A+nh(t ) n A+(t ) − βh + A0nh(t ) n A0(t ) ⎛ −A A++ ⎞ ⎟ + s A++n A++(t ) exp⎜ ⎝ kT ⎠ (A2)

⎛ −A ⎞ dnSTH(t ) = βSTHnh(t ) nST(t ) − sSTHnSTH(t ) exp⎜ STH ⎟ ⎝ dt kT ⎠ − βSTEne(t ) nSTH(t )

(A7)

Meaning of the Terms. In Equation A1, term αt describes the electron−hole creation rate in the crystal under irradiation. Coefficient (1 − rex) indicates that part of the correlated electron−hole pairs giving direct creation of excitons is skipped. Term −βe+A+ne(t) nA+(t) describes electron capture by activator centers A+. The minus sign indicates that such a process leads to decreased free electron concentration. Term −βe+A2+ne(t) nA2+(t) is for electron capture by A2+ centers. The bimolecular capture coefficient in the case of a changed center βe+A2+ is different from that in the case of capture by a neutral center βe+A+. Expression −βSTEne(t) nSTH(t) characterizes electron capture by STH with creation of STE. Term +sA0nA0 exp (−AA0/ (kT)) describes thermal release of electrons from A0. In Equation A2, term αt(1 − rex) is the electron−hole creation rate under irradiation. The expression −βSTHnh(t) nST(t) characterizes self-trapping of holes in regular CsI lattice, i.e., creation of Vk centers. Member −βh+A+nh(t) nA+(t) describes capture of holes by neutral activator centers A+, and term −βh+A0nh(t) nA0(t) describes capture of holes by activator center A0 with electrons. Expressions +sSTHnSTH(t) exp(−ASTH/(kT)) and +sA++nA++(t) exp(−AA++/(kT)) describe thermally activated delocalization of self-trapped holes and holes trapped by the activators, respectively. Equations A3−A5 of the System describe the balance of STHs dnSTH(t)/dt, electrons trapped by activator ions dnA0(t)/ dt, and holes trapped by activator ions dnA++(t)/dt. The terms in the corresponding equations are described above. Equation A6 is for the balance of STEs. The first term βSTEne(t) nSTH(t) describes capture of an electron by selftrapped holes with creation of STE. Term −nSTE(t)/τnr takes into account temperature quenching of STE emission, where STE nonradiative relaxation time 1/τnr = sSTE exp(−ASTE/ (kT)). Term −nSTE(t)/τSTE describes radiative decay of STEs, and +αtrex describes the direct creation of excitons. Equation A7 of the System, which characterizes the balance of excited activator centers, contains a term describing electron capture by A2+ centers βe+A2+ne(t) nA2+(t), a term describing capture of holes by A0 centers βh+A0nh(t) nA0(t), and also a term describing radiative decay of excited activator centers −nA2+(t)/ τA.

APPENDIX A System of rate equations describing concentration kinetics of free electrons ne, free holes nh, self-trapped holes nSTH, electrons captured by activator centers nA0, holes captured by activator centers nA2+, self-trapped excitons nSTE, and excited activator centers nA+*. System of Rate Equations.

⎛ −A ⎞ + sSTHnSTH(t ) exp⎜ STH ⎟ ⎝ kT ⎠

(A6)

dn A+ *(t ) = βh + A0nh(t ) n A0(t ) + βe + A++ne(t ) n A++(t ) dt n + (t ) − A* τA

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⎛ −A A0 ⎞ ⎟ + s A0n A0(t ) exp⎜ ⎝ kT ⎠

(A5)

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(A3)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

⎛ −A A0 ⎞ dn A0(t ) ⎟ = βe + A+ne(t ) n A+(t ) − s A0 n A0(t ) exp⎜ ⎝ kT ⎠ dt − βh + A0nh(t ) n A0(t )

Notes

The authors declare no competing financial interest.

(A4) 20589


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ACKNOWLEDGMENTS We thank FP7 project “Strengthening Ukraine and EU research cooperation in the field of Material Sciences” (SUCCESS). S.G. is grateful for scholarship PALSE in frame of the Avenir LyonSaint-Etienne Programme from University of Lyon. This work was partially financially supported by the RF Ministry of Education and Science under the Agreement RFMEFI61614 × 0006; this support is gratefully acknowledged. We are indebted to Kevin Smith for language corrections.

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